Problem: Which of the following numbers is a factor of 48? ${5,7,10,12,13}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $48$ by each of our answer choices. $48 \div 5 = 9\text{ R }3$ $48 \div 7 = 6\text{ R }6$ $48 \div 10 = 4\text{ R }8$ $48 \div 12 = 4$ $48 \div 13 = 3\text{ R }9$ The only answer choice that divides into $48$ with no remainder is $12$ $ 4$ $12$ $48$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $48$ $48 = 2\times2\times2\times2\times3 12 = 2\times2\times3$ Therefore the only factor of $48$ out of our choices is $12$. We can say that $48$ is divisible by $12$.